Question

1. if m∠abe=(6x + 2)° and m∠dbe=(8x - 14)°, find m∠abe.

m∠abe=

1. if m∠abd=(22n - 11)° and m∠abe=(12n - 8)°, find m∠ebd.

m∠ebd=

Explanation:

Step1: Assume $\angle ABD$ is a straight - angle and $\angle ABE+\angle DBE=\angle ABD = 180^{\circ}$ (if $\angle ABD$ is a straight - angle, the sum of its sub - angles is $180^{\circ}$)

$(6x + 2)+(8x-14)=180$

Step2: Combine like terms

$6x+8x+2 - 14=180$
$14x-12 = 180$

Step3: Add 12 to both sides

$14x=180 + 12$
$14x=192$

Step4: Solve for x

$x=\frac{192}{14}=\frac{96}{7}$

Step5: Find $m\angle ABE$

$m\angle ABE=6x + 2=6\times\frac{96}{7}+2=\frac{576}{7}+2=\frac{576 + 14}{7}=\frac{590}{7}\approx84.29^{\circ}$

For question 16:

Step1: Note that $\angle ABD=\angle ABE+\angle EBD$

So, $\angle EBD=\angle ABD-\angle ABE$

Step2: Substitute the given expressions

$\angle EBD=(22n - 11)-(12n - 8)$

Step3: Simplify the expression

$\angle EBD=22n-11 - 12n + 8$
$\angle EBD=(22n-12n)+(-11 + 8)$
$\angle EBD = 10n-3$

Answer:

1. $m\angle ABE=\frac{590}{7}^{\circ}$
2. $m\angle EBD=(10n - 3)^{\circ}$